We use the quantum renormalization-group（QRG） method to study the entanglement and quantum phase transition（QPT） in the one-dimensional spin-1/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys....We use the quantum renormalization-group（QRG） method to study the entanglement and quantum phase transition（QPT） in the one-dimensional spin-1/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys.（N.Y.） 16 407].We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations.We also investigate the scaling behavior of the system close to the quantum critical point,which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size.Also,the first derivative of concurrence between two blocks diverges at the quantum critical point,which is directly associated with the divergence of the correlation length.展开更多
The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approxi...The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approximation.展开更多
We investigate two-leg Hubbard ladders in the Luttinger liquid regime by the density-matrix renormalization group method. Applicability of the bond concept in this region is discussed in a quantitative comparison of p...We investigate two-leg Hubbard ladders in the Luttinger liquid regime by the density-matrix renormalization group method. Applicability of the bond concept in this region is discussed in a quantitative comparison of power-law decay exponents, energy components and anti-bond occupations between ladders and chains. The interaction between bond and anti-bond bands induced by finite Hubbard repulsion U is emphasized by our numerical results. Our quantitative results are useful for the justification of the validity of various analytical approaches.展开更多
In an analytical way of studying matter effects on neutrino oscillations, the Naumov and Toshev relations have been derived to respectively link the Jarlskog invariant of CP violation and the Dirac phase in the standa...In an analytical way of studying matter effects on neutrino oscillations, the Naumov and Toshev relations have been derived to respectively link the Jarlskog invariant of CP violation and the Dirac phase in the standard parametrization of the 3×3 flavor mixing matrix to their matter-corrected counterparts. Here we show that there exist similar relations for Dirac neutrinos and charged leptons evolving with energy scales via the one-loop renormalizationgroup （RG） equations in the tau-dominance approximation, and for the running behaviors of up- and down-type quarks in the top-dominance approximation, provided a different parametrization is taken into account.展开更多
We study the order parameter probability distribution at the critical point for the three-dimensional spin-1/2 and spin-1 Ising models on the simple cubic lattice under periodic boundary conditions. The finite size sc...We study the order parameter probability distribution at the critical point for the three-dimensional spin-1/2 and spin-1 Ising models on the simple cubic lattice under periodic boundary conditions. The finite size scaling relation for the order parameter probability distribution is tested and verified numerically by microcanonical Creutz cellular automata simulations. The state critical exponent δ, which characterizes the far tail regime of the scaling order parameter probability distribution, is estimated for three-dimensional Ising models using the cellular automaton simulations at the critical temperature. The results are in good agreement with the Monte Carlo calculations.展开更多
We find that there are two time scales t and c In t in the asymptotic behaviour of diffusion process in the porous medium, which give us a new insight to the anomalous dimension in this problem, further we construct a...We find that there are two time scales t and c In t in the asymptotic behaviour of diffusion process in the porous medium, which give us a new insight to the anomalous dimension in this problem, further we construct an iterative method to calculate the anomalous dimension and obtain an improved result,展开更多
The problem of calculating the energy spectrum of turbulent velocity pulsations in the case of homogeneous isotropic and stationary turbulence is considered. The domain of turbulent energy production is treated as “a...The problem of calculating the energy spectrum of turbulent velocity pulsations in the case of homogeneous isotropic and stationary turbulence is considered. The domain of turbulent energy production is treated as “a black box” on which boundary the spectral energy flux is given. It is assumed that the spectrum is formatted due to intermodal interactions being local in the wave-number space that leads to a cascade mechanism of energy transfer along the wave-number spectrum and the possibility of using the renormalization-group method related to the Markovian features of the process under consideration. The obtained formula for energy spectrum is valid in a wide wave-number range and at arbitrary values of fluid viscosity. It is shown that in functional formulation of the statistical theory of turbulence, the procedure of separating local intermodal interactions, which govern energy transfer (straining effect), and filtering out nonlocal interactions, which have no influence on energy transfer (sweeping effect), is directly described without providing additional arguments or conjectures commonly used in the renormalization-group analysis of turbulent spectra.展开更多
An analytical equation of state (EOS) for hard core Asakura-Oosawa (AO) fluid is established by combining the AO potential, the first-order perturbation theory and the radial distribution function (RDF) for the hard s...An analytical equation of state (EOS) for hard core Asakura-Oosawa (AO) fluid is established by combining the AO potential, the first-order perturbation theory and the radial distribution function (RDF) for the hard sphere fluid.The phase equilibria are studied by using the renormalization-group (RG) theory. The obtained results agree well with the simulation data. Investigation shows that the attractive range parameter plays an important role in the phase equilibria for AO fluid.展开更多
文摘We use the quantum renormalization-group（QRG） method to study the entanglement and quantum phase transition（QPT） in the one-dimensional spin-1/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys.（N.Y.） 16 407].We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations.We also investigate the scaling behavior of the system close to the quantum critical point,which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size.Also,the first derivative of concurrence between two blocks diverges at the quantum critical point,which is directly associated with the divergence of the correlation length.
文摘The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approximation.
基金Supported by the National Natural Science Foundation of China under Grant No 10447119.
文摘We investigate two-leg Hubbard ladders in the Luttinger liquid regime by the density-matrix renormalization group method. Applicability of the bond concept in this region is discussed in a quantitative comparison of power-law decay exponents, energy components and anti-bond occupations between ladders and chains. The interaction between bond and anti-bond bands induced by finite Hubbard repulsion U is emphasized by our numerical results. Our quantitative results are useful for the justification of the validity of various analytical approaches.
基金Supported by the National Natural Science Foundation of China(11775231) and (11775232)the National Youth Thousand Talents Programthe CAS Center for Excellence in Particle Physics
文摘In an analytical way of studying matter effects on neutrino oscillations, the Naumov and Toshev relations have been derived to respectively link the Jarlskog invariant of CP violation and the Dirac phase in the standard parametrization of the 3×3 flavor mixing matrix to their matter-corrected counterparts. Here we show that there exist similar relations for Dirac neutrinos and charged leptons evolving with energy scales via the one-loop renormalizationgroup （RG） equations in the tau-dominance approximation, and for the running behaviors of up- and down-type quarks in the top-dominance approximation, provided a different parametrization is taken into account.
文摘We study the order parameter probability distribution at the critical point for the three-dimensional spin-1/2 and spin-1 Ising models on the simple cubic lattice under periodic boundary conditions. The finite size scaling relation for the order parameter probability distribution is tested and verified numerically by microcanonical Creutz cellular automata simulations. The state critical exponent δ, which characterizes the far tail regime of the scaling order parameter probability distribution, is estimated for three-dimensional Ising models using the cellular automaton simulations at the critical temperature. The results are in good agreement with the Monte Carlo calculations.
基金Supported by the National Fundamental Research Programme of China, the Innovation Funds from Chinese Academy of Sciences, the National Natural Science Foundation of China under Grant Nos 60121503 and 10604052. Tu Tao thanks Professor N. Goldenfeld （at UIUC） for helpful discussion.
文摘We find that there are two time scales t and c In t in the asymptotic behaviour of diffusion process in the porous medium, which give us a new insight to the anomalous dimension in this problem, further we construct an iterative method to calculate the anomalous dimension and obtain an improved result,
文摘The problem of calculating the energy spectrum of turbulent velocity pulsations in the case of homogeneous isotropic and stationary turbulence is considered. The domain of turbulent energy production is treated as “a black box” on which boundary the spectral energy flux is given. It is assumed that the spectrum is formatted due to intermodal interactions being local in the wave-number space that leads to a cascade mechanism of energy transfer along the wave-number spectrum and the possibility of using the renormalization-group method related to the Markovian features of the process under consideration. The obtained formula for energy spectrum is valid in a wide wave-number range and at arbitrary values of fluid viscosity. It is shown that in functional formulation of the statistical theory of turbulence, the procedure of separating local intermodal interactions, which govern energy transfer (straining effect), and filtering out nonlocal interactions, which have no influence on energy transfer (sweeping effect), is directly described without providing additional arguments or conjectures commonly used in the renormalization-group analysis of turbulent spectra.
文摘An analytical equation of state (EOS) for hard core Asakura-Oosawa (AO) fluid is established by combining the AO potential, the first-order perturbation theory and the radial distribution function (RDF) for the hard sphere fluid.The phase equilibria are studied by using the renormalization-group (RG) theory. The obtained results agree well with the simulation data. Investigation shows that the attractive range parameter plays an important role in the phase equilibria for AO fluid.
